How to make particle animation intensify as an empty comes near?
Weights on a lattice.



Armature controlling lattice and lattice controls particles.




Particles can be affected by a lattice.  This might prove to be the least CPU resource consuming.  Lattice can be affected by armature or shape keys et cetera.  Higher UVW specifications may produce more controlled effects.
Particles can be affected by forces attached to an empty.  You can use an effector group to minimize force calculation